Name: circuit component scaling for filters
Uploaded: 2024-07-08T13:20:03.000Z
Duration: 1 min 26 s
Channel: JoVE

El escalado de magnitud y frecuencia simplifica el diseño del filtro al calibrar las respuestas del filtro y los parámetros del circuito para que se ajusten a los rangos utilizables.
El escalado de magnitud implica amplificar todas las impedancias de una red por un factor, manteniendo respuestas de frecuencia consistentes.
A continuación, los valores de impedancia y frecuencia escalados se expresan mediante el factor de escala.
Este proceso no altera la frecuencia de resonancia del circuito, el factor de calidad, el ancho de banda o las funciones de transferencia.
El escalado de frecuencia cambia la respuesta de frecuencia de una red, ya sea hacia arriba o hacia abajo en el eje de frecuencia, mientras que la impedancia no cambia. Se logra multiplicando la frecuencia por un factor de escala.
El escalado de frecuencia influye en las impedancias de los elementos reactivos dependientes de la frecuencia, pero la resistencia no se ve afectada.
El factor de escala altera la frecuencia de resonancia y el ancho de banda, pero el factor de calidad sigue siendo el mismo.
Una expresión general para el escalado de impedancia y frecuencia se adapta al escalado simultáneo de magnitud y frecuencia.
Para los casos en los que no se aplica la escala de magnitud, el factor de escala de magnitud se establece en uno. Del mismo modo, sin escalado de frecuencia, el factor de escalado de frecuencia se establece en uno.

respuesta de frecuencia

Al diseñar y analizar filtros, circuitos resonantes o análisis de circuitos en general, puede resultar conveniente trabajar con valores de elementos estándar como 1 ohmio, 1 henrio o 1 faradio antes de escalar estos valores a cifras más realistas. Este enfoque se utiliza ampliamente al no emplear valores de elementos realistas en numerosos ejemplos y problemas; simplifica el dominio del análisis de circuitos a través de valores de componentes convenientes. De este modo se reduce la complejidad de los cálculos, en el entendido de que las técnicas de escalamiento pueden ajustar posteriormente estos valores a niveles más prácticos.
El escalado de un circuito se puede realizar de dos maneras: escalado de magnitud (o impedancia) y escalado de frecuencia. Estos métodos ajustan los componentes del circuito para que funcionen dentro de rangos prácticos. El escalado de magnitud cambia el tamaño de los componentes sin afectar la forma en que el circuito responde a diferentes frecuencias. Por otro lado, el escalado de frecuencia mueve la respuesta del circuito a frecuencias más altas o más bajas en el espectro.
Escalado de magnitud:
El escalado de magnitud implica ajustar los tamaños de los componentes del circuito (como resistencias, inductores y condensadores) mediante un factor determinado, pero sin cambiar la forma en que el circuito responde a diferentes frecuencias. Las impedancias del circuito están en términos de resistencias (R), inductores (L) y condensadores (C) en un circuito. Cuando se aplica la escala de magnitud K_m, estos componentes se transforman de la siguiente manera:
<img alt="Equation 1" src="/files/ftp_upload/15150/15150_Equation_1.svg" style="height: 12px;">
<img alt="Equation 2" src="/files/ftp_upload/15150/15150_Equation_2.svg" style="height: 36px;">
Escalado de frecuencia:
El escalado de frecuencia cambia la respuesta de frecuencia de un circuito a lo largo del eje de frecuencia, ya sea hacia arriba o hacia abajo, sin alterar los niveles de impedancia. Esto se logra multiplicando la frecuencia por un factor de escala, indicado por K_f. Los nuevos valores de la inductancia y la capacitancia están determinados por:
<img alt="Equation 3" src="/files/ftp_upload/15150/15150_Equation_3.svg" style="height: 36px;">
<img alt="Equation 4" src="/files/ftp_upload/15150/15150_Equation_4.svg" style="height: 36px;">
Si un circuito se escala para ambos parámetros: magnitud y frecuencia al mismo tiempo, entonces:
<img alt="Equation 5" src="/files/ftp_upload/15150/15150_Equation_5.svg" style="height: 36px;">
<img alt="Equation 6" src="/files/ftp_upload/15150/15150_Equation_6.svg" style="height: 36px;">
Si los factores de escala de magnitud y frecuencia son iguales, no se produce escala de magnitud ni de frecuencia.

Respuesta de frecuencia

El escalado de magnitud y frecuencia simplifica el diseño del filtro al calibrar las respuestas del filtro y los parámetros del circuito para que se ajusten a los rangos utilizables.
Magnitud...

Education

Educación

JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

Frequency Response

Respuesta en frecuencia

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Scaling

circuit component scaling for filters

Circuit component scaling helps turn simple circuit values into practical ones for filter design and circuit analysis. Engineers often start with standard values like 1 ohm, 1 henry, or 1 farad because they make examples and problems easier to work through. Later, those values can be scaled to more realistic levels.

This method is useful in filters, resonant circuits, and many other circuit analysis problems. It reduces calculation complexity while keeping the circuit behavior easy to study. The idea is to learn the analysis first and then adjust the component values to fit real-world use.

There are two main ways to scale a circuit: magnitude scaling, also called impedance scaling, and frequency scaling. Magnitude scaling changes the size of the components without changing how the circuit responds to different frequencies. Frequency scaling shifts the circuit response higher or lower on the frequency axis without changing the impedance levels.

Magnitude scaling uses a factor called K m to change resistors, inductors, and capacitors. Frequency scaling uses a factor called K f to move the frequency response and to determine new inductance and capacitance values. When both magnitude and frequency scaling are applied together, the circuit can be adjusted in both size and response range. If the magnitude and frequency scaling factors are equal, neither type of scaling occurs.

Circuit Component Scaling for Filters

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scaling

Circuit component scaling helps turn simple circuit values into practical ones for filter design and circuit analysis. Engineers often start with standard values like 1 ohm, 1 henry, or 1 farad because they make examples and problems easier to work through. Later, those values can be scaled to more realistic levels. This method is useful in filters, resonant circuits, and many other circuit analysis problems. It reduces calculation complexity while keeping the circuit behavior easy to study.

design example

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key terms and concepts

Learn how magnitude scaling and frequency scaling adjust resistors, inductors, capacitors, and circuit response for easier filter design and analysis.

Circuit Component Scaling for Filters | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Circuit Component Scaling for Filters

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